JNTU
JNTU B.Tech II AEROSPACE VEHICLE STRUCTURES I Previous Question Paper (September/ October -2023 - R13)
Answer all questions in Part A. Answer any one question from each unit in Part B.
Part A
What do you mean by boundary conditions?
Answer
Boundary conditions are the specific constraints or requirements imposed on a physical system at its spatial or temporal limits. In structural mechanics, they represent the physical support or loading conditions applied to the edges or ends of a structure, such as fixed, pinned, or roller supports, which dictate the displacement or force values at those boundaries to ensure a unique solution to the governing differential equations.
Explain in brief about the Airy’s stress function.
Answer
Airy's stress function is a scalar function, denoted by φ, used to solve two-dimensional plane stress or plane strain problems in elasticity. It simplifies the governing equations of equilibrium and compatibility by expressing the stress components in terms of the derivatives of φ.
For a two-dimensional body in the absence of body forces, the stress components are defined as:
Substituting these into the compatibility equation leads to the biharmonic equation, which the stress function must satisfy:
By solving this biharmonic equation for a given set of boundary conditions, one can determine the stress distribution throughout the structural member.
What do you mean by order of redundancy?
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Explain in brief about statically determinate structure.
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What are the assumptions of the curved beams in flexure?
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Explain in brief about Prandtl’s membrane analogy.
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What do you mean by slenderness ratio?
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Explain the effect of intermediate support on beam column.
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What is Bredt-Batho formula?
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Explain the important characteristics of Rayleigh-Ritz method.
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Part B
A beam of length l, with a thin rectangular cross section, is built-in at the end x=0 and loaded at the tip by a vertical force P. Show that the stress distribution, as calculated by simple beam theory, can be represented by the expression
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A cylindrical pressure vessel has an internal diameter of 2 m and is fabricated from plates 20 mm thick. If the pressure inside the vessel is 1.5 N/mm² and, in addition, the vessel is subjected to an axial tensile load of 2500 kN, calculate the direct and shear stresses on a plane inclined at an angle of 60° to the axis of the vessel. Calculate also the maximum shear stress.
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A beam ABC of length 16 m consists of spans AB and BC each 8 m long and is simply supported at A, B and C. The beam carries uniformly distributed load of 40 kN/m on the whole length. Find the reactions at the supports and the support moments.
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A continuous beam ABC consists of two spans AB and BC of lengths 4 m and 6 m respectively. The span AB carries a point load of 40 kN at 2 m from A. Find the reactions at the supports and draw the bending moment diagram for the beams.
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Determine the maximum bending moment and the maximum deflection of a rail road. Rail is subjected to a single wheel load of 150 kN. The elastic support for the rail has a spring constant of k = 14 MN/m². The moment of inertia of rail is 3700 × 10⁻⁸ m⁴, E = 200 GPa. Also calculate the maximum stress in the rail assuming that the depth of the rail is 200 mm and that the distance of the centroidal axis of the cross-section of the rail from the top surface is 100 mm.
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A simply supported beam AB of span L and uniform section carries a distributed load of intensity varying from zero at A to w₀/unit length at B according to the law
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Calculate the critical load for a strut which is made of a bar circular in section and 5 m long and which is pin-jointed at both ends. The same bar when freely supported gives a mid-span deflection of 10 mm under a load of 80 N at the centre.
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Derive an expression of critical load for a column subjected to eccentric loading.
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State and derive an expression for Maxwell’s reciprocal theorem.
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Write expression for the potential energy for a simply supported beam with uniformly distributed load having whole span of length ‘L’.
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